The prior art is replete with various attempts at solving the problem of clamping two generally cylindrical members, for example tubes or pipes, together. The problem is to provide a clamp which exerts a radially inward force uniformly around the entire circumference of the tubes to be fastened together. While it is relatively straightforward to exert the force over the greater portion of the circumference of the tubes, it is important if a mechanically strong and leak-free connection is to be formed that the force be exerted over the entire circumference of the pipe. To this end, numerous attempts have been made in the prior art to provide rigid pipe couplings; see, for example, U.S. Pat. No. 494,996 to Dwelle in which rigid hinged members are clamped together to grip the pipe. See also U.S. Pat. No. 2,227,551 to Morris which shows clamps having interlocking fingers to be clamped together to exert the force over the entire circumference of the tube. Later patentees realized that it would be preferable to use a somewhat flexible band which would be slightly deformed to more closely match the contours of the pipe to be clamped, thus being more likely to exert the force uniformly around the entire circumference of the pipe. Into this class fall the U.S. Pat. Nos. to Cassel et al 4,056,273 and 3,905,623, as well as that to Foti 4,165,109. All these show provision of clamps which use a plurality of bolts connecting two ends of a band wrapped around a pair of pipes to be joined and having a connection piece interposed therebetween. Typically, the connection piece is formed with an axially extending recess formed between the bolt holes on both its sides so that upon tightening of the bolts the ends of the band will be deformed to fit more closely together within the recesses; force bars may be used to spread the force exerted by tightening the bolts uniformly across the width of the clamp. In some cases, particularly U.S. Pat. No. 4,056,273 to Cassel, the shaping member may also be shaped to coact with the outer circumference of the tube so as to exert a radially inward force thereon by being pulled into the surface of the pipe by the tightening of the bolt(s) simultaneously with deformation of the ends of the band. However, the fact that this deformation is required means that the force exerted upon tightening the bolts is at least partially directed towards this deformation and is not useful in achieving the primary object of the clamp, that is, to exert a generally radially inward force substantially uniformly around the circumference of the tube.